A. Vrij

Hard sphere colloidal dispersions: Viscosity as a function of shear rate and volume fraction

The viscosities of suspensions of sterically stabilized (hard) silica spheres in cyclohexane are reported as a function of shear rate (γ) and volume fraction (6×10−4<φ<0.6). The shear thinning scales according to (ηr−η∞)/(η0−η∞) =1/(1+1.31ηγa3/kT) with limiting low and high shear viscosities described up to φ∼0.35 by η0=1+5/2φ+(4±2)φ2+(42±10)φ3 , η∞=1+5/2φ+(4±2)φ2+(25±7)φ3 . At higher volume fractions the viscosity becomes more sensitive to φ and diverges at φm=0.63±0.02 (γ→0) , φm=0.70±0.02 (γ→∞) . The experimental results compare well with existing hard sphere theories and the data of Krieger (1972) for aqueous lattices. Even at the highest volume fraction neither yield stresses nor shear thickening are observed.

Monodisperse Colloidal Silica Spheres from Tetraalkoxysilanes: Particle Formation and Growth Mechanism

The mechanisms behind the formation and growth of silica particles prepared from tetraalkoxysilanes in alcoholic solutions of water and ammonia were investigated. By analyzing the competitive growth of a dispersion of silica spheres with a bimodal size distribution, it was established that the growth proceeds through a surface reaction-limited condensation of hydrolyzed monomers or small oligomers. By following the hydrolysis of tetraethoxysilane with 13C liquid NMR and the particle growth with time-resolved static light scattering, it was found that both processes were described by the same first-order rate constants. Therefore, despite the fact that the incorporation of hydrolyzed monomers proceeds through a reactionlimited process, the overall rate of the particle growth is limited by the first-order hydrolysis rate of the alkoxide. It was concluded that the particle formation (or particle nucleation) proceeds through an aggregation process of siloxane substructures that is influenced strongly by the surface potential of the silica particles and the ionic strength of the reaction medium. These conclusions were based on the dependence of the particle stability and final particle size on additions of LiN03 to the reaction and dispersion medium and the independence of the growth rate on the same additions. 0 1992

Preparation and properties of nonaqueous model dispersions of chemically modified, charged silica spheres

Abstract We describe the preparation and properties of a novel type of stable dispersion in weakly polar organic solvents of monodisperse, charged silica spheres coated with 3-methacryloxypropyltrimethoxysilane. An important feature of this silica is that it can be optically matched up to high particle volume fractions. Colloidal crystallization is observed in these dispersions as well as the formation of a glass-like phase. We conclude that this silica provides a very appropriate model dispersion for light-scattering studies on concentrated systems of charged particles.

Interactions in mixtures of colloidal silica spheres and polystyrene molecules in cyclohexane: I. Phase separations

Abstract Phase separations in dispersions of different types of spherical, lyophilic, monodisperse silica particles and polystyrene molecules in cyclohexane at the theta temperature were investigated. We used silica particles stabilized with a chemically bonded layer of stearyl alcohol molecules and silica particles stabilized with tetraethylenepentamine-terminated polyisobutene molecules. At a fixed silica concentration (1.0 or 5.0% w/v) a liquid-liquid phase separation occurs above some limiting polystyrene concentration. The limiting concentration, c lim , usually is of the order of a few percent (w/v), and depends on the molar mass of the polymer. High-molar-mass polymers show a lower c lim value than low-molar-mass polymers. An increase in the concentration of the silica particles lowers the c lim value. The radius of the silica particles also influences c lim . The experimental results are interpreted in terms of a simple “hard sphere-cavity” model, with which a theory is worked out which is based on first principles only. Most experimental results can be reproduced by theoretical calculations on a semiquantitative scale. Discrepancies between theory and experiment only are found with the silica samples that obviously do not conform to the hard sphere model used.

Mode amplitudes in dynamic light scattering by concentrated liquid suspensions of polydisperse hard spheres

This paper concerns the dynamic light scattering by suspensions of polydisperse hard spherical particles. It is concluded that for relatively high volume fractions and fairly narrow distributions, the light scattering correlation function should, to a good degree of approximation, be composed of two independent modes with well‐separated decay times. The faster decaying mode describes collective stochastic compression–dilation motions and is present even for a monodisperse system. The slower decaying mode describes the exchange of different species. The relative mode amplitudes are calculated in the Percus–Yevick approximation for hard spheres. The two decay times of fast and slow mode are associated with diffusion coefficients D+ and D−, respectively. In the case of scattering power polydispersity D+ and D− are rigorously identified with collective and self‐diffusion, respectively. In the case of size polydispersity D+ and D− can be associated with ‘‘average’’ collective and self‐diffusion coefficients. T...

Mixtures of hard spheres in the Percus–Yevick approximation. Light scattering at finite angles

In a previous paper (I), a new equation for the light scattering (or small angle x‐ray or neutron scattering) of a concentrated p‐component mixture of spherical (colloidal) particles in a low‐molecular weight solvent was derived. Use was made of Baxter’s factorization of the direct correlation matrix. It was found that the light scattering intensity can be formulated in factorized form as well. The formalism was applied to a multicomponent system of hard spheres treated in the Percus–Yevick approximation. For zero scattering angle, a rather simple, exact expression was obtained. In this paper it is proved that a closed expression can also be obtained for finite scattering angles. It contains at most 18 (averaged) functions of the scattering angle for any number of hard sphere components. This makes it possible to apply the equation to a continuous distribution of hard sphere diameters. A series expansion is given for small scattering wave numbers.

I. Transition regions, line tensions and contact angles in soap films

Summary An analysis is given of the thickness profile of a circular soap film and its Plateau border. It shows that in principle the thickness as a function of the radial distance, h(r), for a single film, can provide details of the interaction free energy ΔF(h) over a large range of h. The transition region between film and Plateau border where h(r) rapidly changes from microscopic to macroscopic values contains most information. With a simple model of ΔF(h), the profile and extension of the transition region is calculated for some “first black” soap films. It is shown that to complete the macroscopic description of a liquid sheet, a line tension must be introduced. A theoretical expression for this line tension is given and its physical meaning is discussed. Some values are calculated using the same ΔF (h) as before.

Light scattering of a concentrated multicomponent system of hard spheres in the Percus–Yevick approximation

A formalism for light scattering (or small angle x‐ray or neutron scattering) from a (concentrated) multicomponent system of spherical (colloidal) particles dispersed in a low‐molecular weight solvent is derived in terms of direct correlation functions introduced by Ornstein and Zernike and also in terms of Q functions introduced by Baxter. These functions, which characterize the interparticle interactions, are often theoretically much more accessible than the more familiar pair‐distribution functions. The formalism is applied to a multicomponent system of hard spheres treated in the Percus–Yevick approximation. For zero scattering angle, a rather simple, exact expression can be formulated containing mean products of particle diameter and particle scattering amplitude. Some limiting cases are treated in more detail. A series expansion in the particle concentration is given up to the order for which the PY approximation is exact. The influence of polydispersity on light scattering is illustrated for a (gen...

Polydispersity effects in the small‐angle scattering of concentrated solutions of colloidal spheres

Calculations are presented of the intensity of radiation scattered by a polydisperse system of spherical particles at finite concentrations where interparticle interference of the scattered waves becomes important. The results apply to small‐angle (x‐ray and neutron) scattering and to light scattering of a solution of particles in the colloidal size range. Use is made of a closed expression for the scattering of a multicomponent mixture of hard spheres recently derived by one of us. The derivation is based on Baxter’s solution of the Percus–Yevick approximation for hard sphere fluids.

Determination of static and dynamic interactions between monodisperse, charged silica spheres in an optically matching, organic solvent

A light scattering study is presented on static and dynamic interactions between monodisperse, charged silica spheres suspended in an optically matching, salt free mixture of ethanol and toluene up to volume fractions of 10%. The static structure factor S(K), well described by calculations in the RMSA approximation, is combined with the wave vector (K) dependent (short‐time) diffusion coefficient De(K) to give the function H(K) which represents the hydrodynamic interactions. From H(K), obtained for the first time for charged particles, we conclude that the long‐range electrostatic repulsion between the spheres has a pronounced influence on the hydrodynamics of large‐scale, collective particle motions, whereas small‐scale single‐particle diffusion is relatively unaffected.